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Chapter 0: Problem 131

If \(n>0,\) then \(-|n|=\) _____ .

Short Answer

Expert verified
-n

Step by step solution

01

Understand the Absolute Value

The absolute value of a number is always non-negative. For any positive number \(n\), \(|n|\) is simply \(n\).
02

Apply the Absolute Value

Given \(n > 0\), we determine that \(|n| = n\).
03

Find the Negative of the Absolute Value

To find \(-|n|\), substitute \(|n|\) with \(n\) from the previous step. Therefore, \(-|n| = -n\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Absolute Value
Absolute value is a concept in mathematics that refers to the distance of a number from zero on the number line.
It does not take into account whether the number is positive or negative.
Instead, it simply measures how far the number is from zero.
Mathematically, the absolute value of a number is denoted by two vertical bars on either side of the number, such as \(|-n|\) or \(|n|\).
For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5.
This is because both -5 and 5 are five units away from zero on the number line.
Absolute value function is particularly useful in various algebraic expressions and equations to simplify and solve them accurately.
Dealing with Negative Values
In algebra, negative values represent numbers less than zero.
These numbers are situated to the left of zero on the number line.
When dealing with negative values in the context of absolute value, it's important to recognize that the absolute value will convert these negatives into their positive counterparts.
For instance, if you have \(-|n|\), here \(-|n|\) means we first take the absolute value which will be positive, and then we multiply by -1 to regain the negative sign.
Generally, whenever you see \(-|n|\) with \(|n|\) representing the absolute value, it markedly makes the number originally positive into negative form.
Working with Positive Numbers
Positive numbers are those greater than zero and are located to the right of zero on the number line.
When calculating the absolute value of a positive number, the number remains unchanged.
For instance, if \(|n| = n\) and \(|5| = 5\), the absolute value of 5 is plainly 5.
To further explain, if we have an equation where \(|n|\) is involved and we know \(|n| = n\), finding the negative of this absolute value means we simply make \(-|n|\) turn into \-n\.
It's fundamental to grasp that the sign \-\ before an absolute value implies changing the final value to its opposite sign, which is crucial in calculations where negative results are expected.

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Most popular questions from this chapter

Multiply and simplify. Assume that all variable expressions represent positive real numbers. $$ (2 \sqrt{3}+\sqrt{7})(2 \sqrt{3}-\sqrt{7}) $$

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Multiply and simplify. Assume that all variable expressions represent positive real numbers. $$ (6 z-\sqrt{5})^{2} $$

If \(n<0,\) then \(-|n|=\) _____.

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